Eleven spherically symmetric constant density solutions with cosmological constant

Abstract

Einstein's field equations with cosmological constant are analysed for a static, spherically symmetric perfect fluid having constant density. Five new global solutions are described. One of these solutions has the Nariai solution joined on as an exterior field. Another solution describes a decreasing pressure model with exterior Schwarzschild-de Sitter spacetime having decreasing group orbits at the boundary. Two further types generalise the Einstein static universe. The other new solution is unphysical, it is an increasing pressure model with a geometric singularity.

19 pages, 5 figures, 1 table, revised bibliography, corrected eqn. (3.11), typos corrected, two new references

References in corpus (3)

• Discovery of a Supernova Explosion at Half the Age of the Universe and its Cosmological Implications
• Gravitational Equilibrium in the Presence of a Positive Cosmological Constant
• The Consistent Newtonian Limit of Einstein's Gravity with a Cosmological Constant

Cited by in corpus (60)

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• Stability of the Einstein static universe in f(R) gravity
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• A causal Schwarzschild-de Sitter interior solution by gravitational decoupling
• Stability of the Einstein static Universe in $f(R,T)$ gravity
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• Light escape cones in local reference frames of Kerr-de Sitter black hole spacetimes and related black hole shadows
• Anisotropic ultracompact Schwarzschild star by gravitational decoupling
• Einstein static Universe in hybrid metric-Palatini gravity
• Tolman-Oppenheimer-Volkoff equations in presence of the Chaplygin gas: stars and wormhole-like solutions
• General relativistic polytropes with a repulsive cosmological constant
• Einstein static universes are unstable in generic f(R) models
• Pseudo-Newtonian and general relativistic barotropic tori in Schwarzschild-de Sitter spacetimes
• Stability of the Einstein static universe in IR modified Hořava gravity
• Physics of dark energy particles
• Gravitational instability of polytropic spheres containing region of trapped null geodesics: a possible explanation of central supermassive black holes in galactic halos
• Does the cosmological constant imply the existence of a minimum mass?
• Scale-dependent polytropic black hole
• Astrophysical Configurations with Background Cosmology: Probing Dark Energy at Astrophysical Scales
• Dust Static Spherically Symmetric Solution in $f(R)$ Gravity
• Stable Schwarzschild stars as black-hole mimickers
• On the Stability of Jordan-Brans-Dicke Static Universe
• Polytropic spheres containing regions of trapped null geodesics
• Dynamical instability of fluid spheres in the presence of a cosmological constant
• The Einstein static universe in Scalar-Fluid theories
• Einstein Static Universe in Braneworld Scenario
• Bounds on M/R for Charged Objects with positive Cosmological constant
• Emergent universe in Horava-Lifshitz-like F(R) gravity
• Photon motion in Kerr-de Sitter spacetimes
• Static trace free Einstein equations and stellar distributions
• Bounds on M/R for static objects with a positive cosmological constant
• Relativistic Compact Objects in Isotropic Coordinates
• Current-carrying string loops in black-hole spacetimes with a repulsive cosmological constant
• Perfect fluid spheres with cosmological constant
• On astrophysical bounds of the cosmological constant
• Acceleration of string loops in the Schwarzschild-de Sitter geometry
• Induced Matter Brane Gravity and Einstein Static Universe
• Einstein static Universe in non-minimal kinetic coupled gravity
• Stability of Einstein Static Universe over Lyra Geometry
• Dynamical instability of polytropic spheres in spacetimes with a cosmological constant
• Extended Tolman III and VII solutions in $f(\mathcal{R},T)$ gravity: Models for neutron stars and supermassive stars
• Lensing in an interior Kottler solution
• Spherically symmetric solutions and gravitational collapse in brane-worlds
• Equilibrium of large astrophysical structures in the Newton-Hooke spacetime
• Radial instability of trapping polytropic spheres
• Polytropic spheres modelling dark matter halos of dwarf galaxies
• Recessional velocities and Hubble's law in Schwarzschild-de Sitter space
• Superluminal velocities in Schwarzschild-de Sitter space
• Buchdahl type inequalities in $d$-dimensions
• From Global to Local Dynamics: Effects of the Expansion on Astrophysical Structures
• A new two-sphere singularity in general relativity
• Charged perfect fluids in the presence of a cosmological constant
• Slowly rotating Tolman VII solution
• Generating exact polytropes in non-conservative unimodular geometries
• Trapping of null geodesics in slowly rotating spacetimes
• An exact static two-mass solution using Nariai spacetime
• On a weak Gauss law in general relativity and torsion
• The Tolman VII Space-time in the Presence of a Charge and a Cosmological Constant